Question

The distance between the points (m, -n) and (-m,n)​

Answer 1

Step-by-step explanation:

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Answer 2

The distance between the points (m, -n) and    (-m,n) = $2\sqrt{m^{2}+n^{2}}$

Step-by-step explanation:

The distance between any two points $A(x_{1},y_{1}) \ \& \ B(x_{2}, y_{2})$ is given by the formula:

AB =  $\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Now, let the two points (m,-n) & (-m, n) be A(m,-n) and B(-m,n).

Then, comparing them with the points in the formula, we get:

                $x_{1} = m\\x_{2} = -m\\y_{1} = -n\\y_{2} = n$

So,  putting the values in the formula, the distance between the given two points will be:

AB = $\sqrt{[(-m)-m]^{2}+[n-(-n)]^{2}}$

     = $\sqrt{(-m-m)^{2}+(n+n)]^{2}}$

     = $\sqrt{(-2m)^{2}+(2n)]^{2}}$

     = $\sqrt{4m^{2}+4n^{2}}$

     = $\sqrt{4(m^{2}+n^{2})}$

     = $2\sqrt{m^{2}+n^{2}}$ [ As distance is always positive.]

We get, AB = $2\sqrt{m^{2}+n^{2}}$

That is,

The distance between the given two points (m,-n) and (-m,n) = $2\sqrt{m^{2}+n^{2}}$